(1) There are n ropes and your task is to tie them into a single rope. The i'th rope is of length li (for i = 1,...,n). When you tie two rope segments, they become joined into one rope segment and you pay a cost equal to the sum of their lengths. Design an efficient algorithm to find a sequence of joining operations that combines the n ropes into a single rope that minimizes the combined cost. Your algorithm should output the sequence of operations, and the minimum cost.

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Typically, the clearest way to explain an algorithm is in English, with the use of some notation. A clear explanation followed by annotated pseudo-code is also fine.

pls send me solution fast within  5 minutes and i will like for sure.

solution musst be in typed form.

Remember that when a problem asks you to design an algorithm, you must also prove the algorithm’s correctness and analyze its running time, i.e., the running time must be bounded by a polynomial function of the input size.

 

 

 

(1)
There are n ropes and your task is to tie them into a single rope. The i'th rope is of
length lį (for i = 1,...,n). When you tie two rope segments, they become joined into one rope segment
and you pay a cost equal to the sum of their lengths. Design an efficient algorithm to find a sequence
of joining operations that combines the n ropes into a single rope that minimizes the combined cost.
Your algorithm should output the sequence of operations, and the minimum cost.
Example: Suppose you have ropes A, B, C, D, E with lengths 2, 4, 5, 3, 8 respectively, and that you
join B and C into segment BC with length 9, then you join D and E into segment DE with length 11,
then you join A with BC to form ABC with length 11, and finally you join ABC to DE to form a rope of
length 22 containing all of the segments. Then the total cost would be 9+11+11+22
53. The process
of joining the segments can be represented pictorially by a binary tree, as illustrated in Figure 2.
D
(1
22
O
A
wa
9
=
Figure 1: Binary tree corresponding to the example discussed. The internal nodes are labelled by the
lengths of the segments to which they correspond.
Transcribed Image Text:(1) There are n ropes and your task is to tie them into a single rope. The i'th rope is of length lį (for i = 1,...,n). When you tie two rope segments, they become joined into one rope segment and you pay a cost equal to the sum of their lengths. Design an efficient algorithm to find a sequence of joining operations that combines the n ropes into a single rope that minimizes the combined cost. Your algorithm should output the sequence of operations, and the minimum cost. Example: Suppose you have ropes A, B, C, D, E with lengths 2, 4, 5, 3, 8 respectively, and that you join B and C into segment BC with length 9, then you join D and E into segment DE with length 11, then you join A with BC to form ABC with length 11, and finally you join ABC to DE to form a rope of length 22 containing all of the segments. Then the total cost would be 9+11+11+22 53. The process of joining the segments can be represented pictorially by a binary tree, as illustrated in Figure 2. D (1 22 O A wa 9 = Figure 1: Binary tree corresponding to the example discussed. The internal nodes are labelled by the lengths of the segments to which they correspond.
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